Properties

Level 2
Symmetry odd
Weight 0
Character \( \chi_{2}(1,\cdot) \)
Multiplicity 1
Precision 3e-09
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues 1,-1

Related objects

Nearby objects

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Downloads

Spectral parameter

$R= 5.41733480684$

The first few Fourier Coefficients

n c(n)
0  0
1  1.0
2  0.7071067
3 -0.3805385
4  0.5
5 -0.2538124
6 -0.2690814
7  0.3976005
8  0.3535533
9 -0.8551903
10 -0.1794725
11  1.2018339
12 -0.1902692
13 -0.9487032
14  0.281146
15  0.0965854
16  0.25
17  0.4728073
18 -0.6047109
19 -0.2312566
20 -0.1269062
21 -0.1513023
22  0.8498249
23  0.3980773
24 -0.1345407
25 -0.9355792
26 -0.6708344
27  0.7059715
28  0.1988002
29  0.8302995
30  0.0682962
31 -0.9855338
32  0.1767766
33 -0.4573441
34  0.3343252
35 -0.1009159
36 -0.4275951
37  1.2173459
38 -0.1635231
39  0.3610181
40 -0.0897362
41 -1.2138931
42 -0.1069869
43 -0.208503
44  0.6009169
45  0.2170579
46  0.2814832
47  0.8729053
48 -0.0951346
49 -0.8419137
50 -0.6615544
51 -0.1799214
52 -0.4743515
53  1.0103675
54  0.4991972
55 -0.3050404
56  0.140573
57  0.088002
58  0.5871104
59 -0.8231248
60  0.0482927
61  0.1413755
62 -0.6968776
63 -0.3400241
64  0.1249999
65  0.2407927
66 -0.3233911
67  1.6113986
68  0.2364036
69 -0.1514837
70 -0.0713583
71 -0.6620648
72 -0.3023554
73 -1.5245189
74  0.8607935
75  0.3560239
76 -0.1156283
77  0.4778498
78  0.2552784
79  0.4661767
80 -0.0634531
81  0.5865409
82 -0.858352
83 -0.4976173
84 -0.0756511
85 -0.1200044
86 -0.1474339
87 -0.315961
88  0.4249125
89  0.31584
90  0.1534832
91 -0.3772052
92  0.1990386
93  0.3750336
94  0.6172373
95  0.0586958
96 -0.0672703
97 -0.1623579
98 -0.5953229
99 -1.0277968
100 -0.4677896
101  0.1285337
102 -0.1272236
103  1.6429478
104 -0.3354172
105  0.0384024
106  0.7144377
107  0.5903261
108  0.3529857
109 -1.1939015
110 -0.2156961
111 -0.463247
112  0.0994001
113 -0.7597877
114  0.0622268
115 -0.1010369
116  0.4151497
117  0.8113218
118 -0.5820371
119  0.1879884
120  0.0341481
121  0.4444049
122  0.0999674
123  0.461933
124 -0.4927668
125  0.4912741
126 -0.2404334
127 -1.1445695
128  0.0883883
129  0.0793434
130  0.1702661
131 -0.7690994
132 -0.228672
133 -0.0919477
134  1.1394309
135 -0.1791843
136  0.1671626
137  0.3608565
138 -0.1071152
139  1.5402981
140 -0.0504579
141 -0.3321741
142 -0.4681505
143 -1.1401838
144 -0.2137975
145 -0.2107403
146 -1.0779977
147  0.3203807
148  0.6086729
149  0.1237454
150  0.2517471
151  1.1980214
152 -0.0817615
153 -0.4043404
154  0.3378907
155  0.2501409
156  0.1805085
157 -0.9080577
158  0.3296368
159 -0.3844838
160 -0.0448681
161  0.1582757
162  0.4147471
163 -1.0123215
164 -0.6069465
165  0.1160796
166 -0.3518686
167  1.1349977
168 -0.0534934
169 -0.0999621
170 -0.0848559
171  0.1977684
172 -0.1042515
173  1.580219
174 -0.2234181
175 -0.3719868
176  0.3004585
177  0.3132307
178  0.2233327
179 -1.9444237
180  0.1085289
181 -0.512271
182 -0.2667241
183 -0.0537988
184  0.1407415
185 -0.3089774
186  0.2651888
187  0.5682358
188  0.4364527
189  0.2806946
190  0.0415042
191  0.5651235
192 -0.0475673
193  0.7854387
194 -0.1148044
195 -0.0916308
196 -0.4209569
197 -1.3421959
198 -0.7267621
199  0.884566
200 -0.3307772
201 -0.6131993
202  0.0908871
203  0.3301275
204 -0.0899607
205  0.3081012
206  1.1617395
207 -0.3404319
208 -0.2371757
209 -0.2779321
210  0.0271546
211 -0.0475778
212  0.5051839
213  0.2519413
214  0.4174236
215  0.0529206
216  0.2495986
217 -0.3918487
218 -0.8442158
219  0.5801382
220 -0.1525202
221 -0.4485538
222 -0.3275651
223 -1.5393704
224  0.0702865
225  0.8000983
226 -0.5372511
227  0.9128879
228  0.044001
229  0.9019606
230 -0.0714439
231 -0.1818403
232  0.2935552
233  0.7939707
234  0.5736912
235 -0.2215544
236 -0.4115624
237 -0.1773983
238  0.1329278
239 -0.8610401
240  0.0241463
241 -1.0508372
242  0.3142417
243 -0.9291729
244  0.0706877
245  0.2136882
246  0.326636
247  0.2193939
248 -0.3484388
249  0.1893625
250  0.3473832
251  1.448663
252 -0.170012
253  0.4784229
254 -0.8093329
255  0.0456663
256  0.0625
257 -0.260423
258  0.0561042
259  0.4840172
260  0.1203963
261 -0.710064
262 -0.5438354
263  0.1406254
264 -0.1616953
265 -0.2564441
266 -0.0650168
267 -0.1201893
268  0.8056993
269 -1.3430298
270 -0.1267024
271  0.980472
272  0.1182018
273  0.143541
274  0.2551641
275 -1.1244108
276 -0.0757418
277  0.6565242
278  1.0891552
279  0.842819
280 -0.0356792
281  0.7908607
282 -0.2348826
283 -0.9044752
284 -0.3310323
285 -0.0223359
286 -0.8062316
287 -0.4826445
288 -0.1511777
289 -0.7764532
290 -0.1490159
291  0.0617834
292 -0.7622595
293  1.1999234
294  0.2265432
295  0.2089193
296  0.4303967
297  0.8484605
298  0.0875013
299 -0.3776572
300  0.178012
301 -0.0829009
302  0.8471291
303 -0.048912
304 -0.0578141
305 -0.0358828
306 -0.2859117
307 -0.6307699
308  0.2389249
309 -0.625205
310  0.1768762
311 -0.2545904
312  0.1276392
313 -0.5300631
314 -0.6420931
315  0.0863023
316  0.2330883
317  0.194188
318 -0.271871
319  0.9978822
320 -0.0317266
321 -0.2246417
322  0.1119178
323 -0.1093398
324  0.2932704
325  0.8875869
326 -0.7158194
327  0.4543255
328 -0.429176
329  0.3470676
330  0.0820807
331  0.9726177
332 -0.2488086
333 -1.0410625
334  0.8025646
335 -0.408993
336 -0.0378255
337 -1.0233143
338 -0.0706839
339  0.2891286
340 -0.0600021
341 -1.1844479
342  0.1398434
343 -0.7323459
344 -0.0737169
345  0.0384484
346  1.1173836
347  0.8702403
348 -0.1579804
349  0.8451607
350 -0.2630343
351 -0.6697574
352  0.2124562
353  1.7182171
354  0.2214875
355  0.1680401
356  0.15792
357 -0.0715369
358 -1.3749151
359 -0.2705691
360  0.0767417
361 -0.9465202
362 -0.3622303
363 -0.1691132
364 -0.1886024
365  0.3869419
366 -0.0380415
367 -1.1515706
368  0.0995193
369  1.0381097
370 -0.2184801
371  0.4017227
372  0.1875168
373  0.736465
374  0.4018034
375 -0.1869487
376  0.3086186
377 -0.7877078
378  0.198481
379 -0.436187
380  0.0293479
381  0.4355529
382  0.3996026
383  0.2118372
384 -0.0336351
385 -0.1212842
386  0.5553891
387  0.1783097
388 -0.081179
389 -1.7276053
390 -0.0647928
391  0.1882138
392 -0.2976614
393  0.2926719
394 -0.9490758
395 -0.1183214
396 -0.5138983
397  0.7493131
398  0.6254828
399  0.0349896
400 -0.2338947
401 -0.2290894
402 -0.4335974
403  0.934979
404  0.0642668
405 -0.1488714
406  0.2334354
407  1.4630476
408 -0.0636118
409 -0.2675291
410  0.2178604
411 -0.1373198
412  0.8214739
413 -0.3272748
414 -0.2407217
415  0.1263014
416 -0.1677086
417 -0.5861428
418 -0.1965276
419 -1.5433967
420  0.0192012
421  0.0572228
422 -0.0336426
423 -0.7465002
424  0.3572188
425 -0.4423486
426  0.1781493
427  0.0562109
428  0.2951631
429  0.4338838
430  0.0374205
431  1.5297266
432  0.1764928
433  0.6379213
434 -0.2770789
435  0.0801948
436 -0.5969507
437 -0.0920581
438  0.4102196
439  0.0192332
440 -0.1078481
441  0.7199966
442 -0.3171754
443 -0.9090201
444 -0.2316235
445 -0.0801641
446 -1.0884993
447 -0.0470899
448  0.0497
449  1.4027601
450  0.5657549
451 -1.458898
452 -0.3798938
453 -0.4558933
454  0.6455092
455  0.0957393
456  0.0311134
457 -0.7717667
458  0.6377825
459  0.3337884
460 -0.0505184
461  0.5935991
462 -0.1285805
463 -0.8466506
464  0.2075748
465 -0.0951881
466  0.561422
467  0.6378113
468  0.4056609
469  0.640693
470 -0.1566625
471  0.3455506
472 -0.2910185
473 -0.250586
474 -0.1254394
475  0.2163589
476  0.0939942
477 -0.8640566
478 -0.6088473
479  0.1460634
480  0.017074
481 -1.1549
482 -0.7430541
483 -0.0602299
484  0.2222023
485  0.0412084
486 -0.6570245
487  0.9681174
488  0.0499838
489  0.3852273
490  0.1511004
491  0.4292236
492  0.2309665
493  0.3925717
494  0.1551349
495  0.2608676
496 -0.2463834
497 -0.2632373
498  0.1338995
499  1.3505352

Plot of the Maass form in a fundamental domain